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Simplifying 3x2 + -21x + 2x + -14 = 6x + -11 Reorder the terms: -14 + -21x + 2x + 3x2 = 6x + -11 Combine like terms: -21x + 2x = -19x -14 + -19x + 3x2 = 6x + -11 Reorder the terms: -14 + -19x + 3x2 = -11 + 6x Solving -14 + -19x + 3x2 = -11 + 6x Solving for variable 'x'. Reorder the terms: -14 + 11 + -19x + -6x + 3x2 = -11 + 6x + 11 + -6x Combine like terms: -14 + 11 = -3 -3 + -19x + -6x + 3x2 = -11 + 6x + 11 + -6x Combine like terms: -19x + -6x = -25x -3 + -25x + 3x2 = -11 + 6x + 11 + -6x Reorder the terms: -3 + -25x + 3x2 = -11 + 11 + 6x + -6x Combine like terms: -11 + 11 = 0 -3 + -25x + 3x2 = 0 + 6x + -6x -3 + -25x + 3x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -3 + -25x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1 + -8.333333333x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -8.333333333x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -8.333333333x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -8.333333333x + x2 = 0 + 1 -8.333333333x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -8.333333333x + x2 = 1 The x term is -8.333333333x. Take half its coefficient (-4.166666667). Square it (17.36111111) and add it to both sides. Add '17.36111111' to each side of the equation. -8.333333333x + 17.36111111 + x2 = 1 + 17.36111111 Reorder the terms: 17.36111111 + -8.333333333x + x2 = 1 + 17.36111111 Combine like terms: 1 + 17.36111111 = 18.36111111 17.36111111 + -8.333333333x + x2 = 18.36111111 Factor a perfect square on the left side: (x + -4.166666667)(x + -4.166666667) = 18.36111111 Calculate the square root of the right side: 4.284986711 Break this problem into two subproblems by setting (x + -4.166666667) equal to 4.284986711 and -4.284986711.Subproblem 1
x + -4.166666667 = 4.284986711 Simplifying x + -4.166666667 = 4.284986711 Reorder the terms: -4.166666667 + x = 4.284986711 Solving -4.166666667 + x = 4.284986711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.166666667' to each side of the equation. -4.166666667 + 4.166666667 + x = 4.284986711 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + x = 4.284986711 + 4.166666667 x = 4.284986711 + 4.166666667 Combine like terms: 4.284986711 + 4.166666667 = 8.451653378 x = 8.451653378 Simplifying x = 8.451653378Subproblem 2
x + -4.166666667 = -4.284986711 Simplifying x + -4.166666667 = -4.284986711 Reorder the terms: -4.166666667 + x = -4.284986711 Solving -4.166666667 + x = -4.284986711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.166666667' to each side of the equation. -4.166666667 + 4.166666667 + x = -4.284986711 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + x = -4.284986711 + 4.166666667 x = -4.284986711 + 4.166666667 Combine like terms: -4.284986711 + 4.166666667 = -0.118320044 x = -0.118320044 Simplifying x = -0.118320044Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.451653378, -0.118320044}
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